The Cauchy property of the generalised Perron intergrals

Abstract

1. Saks calls an integral complete if it satisfies two conditions, of which one, the condition (C), is as follows.If f(x) is defined in (a, b) and is integrable in each interval (a + ε, b − η), where a < a + ε < b − η < b, andexists, then f(x) is integrable in (a, b) and the integral over (a, b) is equal to the above limit.